Effects of Dynamic Perturbations on Optical Spectra of Impurities in Insulators

Abstract

Detailed expressions, derived from a phenomenological Hamiltonian, are given for optical spectra of experimental and theoretical interest for a two-level impurity complex in interaction with the quantized phonon field of lattice vibrations. These results can readily be extended to treat other quantized impurity-perturbing fields which, like the electromagnetic and lattice-vibration fields, have classical analogs (Bose-Einstein statistics). The formulas indicate how different properties of the spectral line are interrelated through the system Hamiltonian and how parameters of that Hamiltonian relate to measurable effects induced by external static stresses. The relationship of the semiclassical Franck-Condon approach (valid for strong phonon-impurity interactions) to the purely quantum treatment (necessary for an accurate analysis of weak perturbations and "motional narrowing") is discussed in detail. It is shown how the results relate to various models proposed to describe Urbach's rule and in particular how the Toyozawa-Mahr model follows from the semiclassical spectral formulas. With only minor midifications, the mathematical expressions can also be used to interpret spin-resonance spectra.